Given:
Base of smaller figure = 20 cm
Area of smaller figure = 320 cm²
Base of the larger figure = 25 cm
To find:
The area of the larger figure.
Solution:
We know that the areas of the similar figure are proportional to the square of corresponding sides of them.
Let A be the area of the larger figure.
[tex]\dfrac{\text{Area of the larger figure}}{\text{Area of the smaller figure}}=\dfrac{(\text{Base of the larger figure})^2}{(\text{Base of the smaller figure})^2}[/tex]
[tex]\dfrac{A}{320}=\dfrac{(25)^2}{(20)^2}[/tex]
[tex]\dfrac{A}{320}=\dfrac{625}{400}[/tex]
[tex]\dfrac{A}{320}=\dfrac{25}{16}[/tex]
Multiply both sides by 320.
[tex]A=\dfrac{25}{16}\times 320[/tex]
[tex]A=500[/tex]
Therefore, the area of the larger figure is 500 cm².
